In the News (Mon 19 Nov 18)

Vectoranalysis is the multi-dimensional analogue of single-variable calculus.

It states that the integral of the (normal component of the) curl of a vector field over a bounded surface is equal to the integral of the (tangential component of the) vector field along the boundary of the surface.

Vector calculus (also called vectoranalysis) is a field of mathematics concerned with multivariate real analysis of vectors in two or more dimensions.

As already explained, two vectors which are represented by equal and parallel straight lines drawn in the same sense are regarded as identical.

When the sum (or difference) of two vectors is to be further dealt with as a single vector, this may be indicated by the use of curved brackets, e.g.

A polar vector, as it is called, is a magnitude associated with a certain linear direction.

encyclopedia.jrank.org /VAN_VIR/VECTOR_ANALYSIS.html (2704 words)

Vectors(Site not responding. Last check: 2007-10-10)

For vectoranalysis, he asserted "[M]y conviction [is] that its principles will exert a vast influence upon the future of mathematical science." Though the Elements of Dynamic was supposed to have been the first of a sequence of textbooks, Clifford never had the opportunity to pursue these ideas because he died quite young.

The reason for this introduction to vectors is that many concepts in science, for example, displacement, velocity, force, acceleration, have a size or magnitude, but also they have associated with them the idea of a direction.

Graphically, a vector is represented by an arrow, defining the direction, and the length of the arrow defines the vector's magnitude.

The sum of two vectors, A and B, is a vector C, which is obtained by placing the initial point of B on the final point of A, and then drawing a line from the initial point of A to the final point of B, as illustrated in Panel 4.

eta.physics.uoguelph.ca /tutorials/vectors/vectors.html (1631 words)

TABLE OF CONTENTS(Site not responding. Last check: 2007-10-10)

A vector field is a function that assigns a vector to a point in a plane or in space.

The results, contained in the theorems of Green, Gauss and Stokes (the so-called Classical Integration Theorems of Vector Calculus), are all variations of the same theme applied to different types of integration.

Green's Theorem relates the path integral of a vector field along an oriented, simple closed curve in the xy-plane to the double integral of its derivative (to be precise, the curl) over the region enclosed by that curve.

Complex analysis is the branch of mathematics investigating functions of complex numbers, and is of enormous practical use in many branches of mathematics, including applied mathematics.

Sometimes, as in the case of the natural logarithm, it is impossible to analytically continue a holomorphic function to a non-simply connected domain in the complex plane but it is possible to extend it to a holomorphic function on a closely related surface known as a Riemann surface.

There is also a very rich theory of complex analysis in more than one complex dimension where the analytic properties such as power series expansion still remain true whereas most of the geometric properties of holomorphic functions in one complex dimension (such as conformality) are no longer true.

Modes of convergence for random variables and their distributions; central limit theorems; laws of large numbers; statistical large smaple theory of functions of sample moments, sample quantiles, rank statistics, and extreme order statistics; asymptotically efficient estimation and hypothesis testing.

A discussion of linear statistical models in both the full and less-than-full rank cases, the Gauss-Markov theorem, and applications to regression analysis, analysis of variance, and analysis of covariance.

A course aimed at the construction, simplification, analysis, interpretation and evaluation of mathematical models that shed light on problems arising in the physical and social sciences.

In other words, the data vector v is transformed into a Fourier vector f by a rotation and change of scale (represented by the constant multiplier √(2/D) in equation 3.39).

In words, Parseval's theorem states that the length of the data vector may be computed either in the space/time domain (the first coordinate reference frame) or in the Fourier domain (the second coordinate reference frame).

The significance of the theorem is that it provides a link between the two domains which is based on the squared length of the data vector.

research.opt.indiana.edu /Library/FourierBook/ch03.html (4038 words)

Vector Calculus at the University of Zimbabwe(Site not responding. Last check: 2007-10-10)

VectorAnalysis has been described as the language of mechanics and electromagnetism because of its numerous applications to problems in engineering and physics.

The course introduces the student to the methods of vectoranalysis with special emphasis put on the application of vector techniques to practical problems in classical mechanics.

Dimensional analysis is a mathematical tool often applied in physics, chemistry, and engineering to understand physical situations that are so complicated that it is difficult or impossible to derive the underlying differential equations.

This theorem describes how every physically meaningful equation involving n variables can be equivalently rewritten as an equation of n-m dimensionless parameters, where m is the number of fundamental dimensions used.

The p-theorem uses linear algebra: the space of all possible physical units can be seen as a vector space over the rational numbers if we represent a unit as the set of exponents needed for the fundamental units (with a power of zero if the particular fundamental unit is not present).

Topics include the fundamentals of two and three dimensional graphics such as clipping, windowing, and coordinate transformations (e.g., positioning of objects and camera), raster graphics techniques such as line drawing and filling algorithms, hidden surface removal, shading, color, curves and surfaces and animation.

This course presents the principles of statistics that are applied to the analysis of data pertinent to the field of Occupational Therapy.

This course covers an in-depth analysis of the fundamental properties of the real number system, including the completeness property, sequences, limits and continuity, differentiation through the Mean Value Theorem, and the Riemann integral.

The course ends with the application of vector space concepts to field theory in order to prove the impossibility of the three classical geometric problems of squaring the circle, duplicating the cube and trisecting the angle.

Continuation of 214-236, showing applications of functional analysis to differential equations including distributions, generalized functions, semigroups of operators, the variational method, and the Riesz-Schauder theorem.

Acquaints students with the Riemann Zeta-function and its meromorphic continuation, characters and Dirichlet series, Dirichlet's theorem on primes in arithmetic progression, zero-free regions of the zeta function, and the prime number theory.

This would be a good place to try this simulation on the graphical addition of vectors.

Inspection of the graphical representation shows that we place the initial point of the vector -B on the final point the vector A, and then draw a line from the initial point of A to the final point of -B to give the difference C.

A unit vector is one which has a magnitude of 1 and is often indicated by putting a hat (or circumflex) on top of the vector symbol, for example